How does the Nyquist sampling theorem determine the number of samples needed to reconstruct a signal?
Consider a simple telephone conversation: A person (message source) speaks into a telephone receiver (encoder), which converts the sound of the spoken word into an electrical signal. This electrical signal is then transmitted over telephone lines (channel) subject to interference (noise). When the signal reaches the telephone receiver (decoder) at the other end of the line it is converted back into vocal sounds. Finally, the recipient (message receiver) hears the original message.
The Nyquist sampling theorem establishes that an analog signal can be uniquely reconstructed from discrete samples if the signal is band-limited, meaning it contains a finite range of frequencies.
To determine the number of samples required, the theorem uses the signal's bandwidth (B), which represents the maximum frequency range occupied by the signal. According to the theorem, the signal must be sampled at a rate of at least samples per second to ensure accurate reconstruction.12
This requirement is based on the Nyquist interval, which is the maximum time allowed between samples, defined as seconds. By taking samples at this frequency, the original waveform can be represented without loss of information, provided the sampling rate is sufficient to capture the highest frequency component present in the signal.12